Learn English – Why did “sceptical” become “skeptical” in the US

Interesting question :) Reading up on this has been a pretty crazy experience. My conclusions are the following:

• The reason for the change from fulfil to fulfill is attributed to inflection, with the spelling modified to suit the function of the word.
• The reason why it isn't spelt fullfill is similar to why parallel only retains the single 'l' at the end—to curb the apparent fugliness of an '-llell' cluster in words such as unparalleled etc.
• There is also a question of consistency involved.

But, unfortunately, another rule in the AE transition was to preserve the "base" word as much as possible, which is why skill/_skilful in BE became skill/skillful in AE. However, this introduced a cluster of letters in words such as skillfully. To put it mildly, the result of exercise was and remains consistently inconsistent.

A related question on the difference in the AE/BE spellings of propelling covers similar territory. It also points to a WP page detailing the differences between American and British spelling which includes the following section on the madness of doubled consonants:

• The word parallel keeps a single -l- in British English, as in American English (paralleling, unparalleled), to avoid the unappealing cluster -llell-.
• Words with two vowels before a final l are also spelled with -ll- in British English before a suffix when the first vowel either acts as a consonant (equalling and initialled; in the United States, equaling or initialed), or belongs to a separate syllable (British fu•el•ling and di•alled; American fu•el•ing and di•aled).
  • British woollen is a further exception due to the double vowel (American: woolen). Also, wooly is accepted in American English, though woolly prevails in both systems.

There's also a note on -ful and -fil:

In both American and British usages, words normally spelled -ll usually drop the second l when used as prefixes or suffixes, for example full→useful, handful; all→almighty, altogether; well→welfare, welcome; chill→chilblain. The British fulfil and American fulfill are never fullfill or fullfil. Johnson wavered on this issue. His dictionary of 1755 lemmatises distil and instill, downhil and uphill.

The answer to your question is that it is a regional not a generational difference.

Teeter-totter is the most widespread in America. Seesaw is specifically Southern. Dandle is from Rhode Island. Other regional variants include dandle board, teedle board, teeter, teeterboard, tilt, and tilting board. See the Dictionary of American Regional English for details.

Etymologically, the word teeter-totter was formed by reduplication of either titter or totter. It derives from titter, now a dialect form for teeter, and totter, which means the same thing. The OED also attests titter-totter, and says to see the Engl. Dial. Dict. for details. The earliest citation is:

• 1607 R. C[arew] tr. Estienne’s World of Wonders 266
  He played with a little boy at titter-totter.

See-saw is also a reduplicative word, and its earliest citations are also from the 1600s, although a bit later than the previous one. However, those are all just interjections. The first noun use is this one:

• 1704 Swift Mechan. Operat. Spirit Misc. 297
  Then, as they sit, they are in a perpetual Motion of See-saw.

And the first verb citation is this:

• 1712 Arbuthnot John Bull ɪᴠ. vii,
  So they went see-sawing up and down, from one End of the Room to the other.